noun
sake
SAYK/seɪk/
The purpose or benefit for which something is done.
The parent brings medicine through heavy rain for the sick child's sake.

Etymology
Old English sacu meant a legal cause or dispute. The modern purpose or benefit sense survives chiefly in phrases such as “for someone's sake,” meaning “out of regard for”; these constructions were probably modeled on Norse.
In context
and both examples are starting with $10,000 for simplicity's sake.
For the sake of compromise, you can call the /j/ a semivowel.